Last Friday, Jaroslaw Kaczynski, the president's brother and leader of the ruling Law and Justice party, decided to take over from Marcinkiewicz after a string of internal rifts.
The prospect of the twins, both Eurosceptics, holding all executive powers in Poland has raised eyebrows at home and abroad. The appointment must be approved by parliament.
An opinion poll for the Gazeta Wyborcza daily indicated that 60% of Poles believed that concentrating power in the hands of the two brothers would have negative consequences for Poland.
More than 80% of those surveyed said they thought that Marcinkiewicz was doing a good job and only 21% expected Kaczynski to be a good replacement.